The piston of a machine exerts a constant force on a ball as it moves horizontally through a distance of $15cm$. You use a motion detector to measure the speed of five different balls as they come off the piston; the data are shown in the table. Use theory to find two quantities that, when graphed, should give a straight line. Then use the graph to find the size of the piston’s force.

Given info :

The horizontal distance $∆d=15cm$and initial velocity$\left(u\right)=0$

The third equation of motion of kinematics is used to calculate the acceleration of the piston.

$v^2=u^2+2a∆d\left(I\right)$

Substituting the values in the above equation and using the excel sheet, we get the following table

Now, put the acceleration with $1/M$, we get the following graph

using excel, we can estimate the equation as:

$y=59.123x-5.0181\left(II\right)$

We know from newton's second law of motion

"The force acting on an object is equal to the mass of that object times its acceleration"

Therefore,

$F=ma\left(III\right)$

So, $a=\frac{F}{m}$

$a=F.\frac{1}{m}\left(IV\right)$

By comparing the equation $\left(IV\right)$with equation of graph $\left(II\right)$, we can deduce the slope of the graph, which is nothing but force

$Force=slope=\frac{y-value}{x-value}=\frac{294.5}{5}=58.7N$

The size of the piston force, as calculated by the use of graph is$58.9N$